Surface energy and specific heat for a semi-infinite medium

Abstract

The surface-energy density is calculated directly for the special transition via field-theoretic renormalization-group techniques to two-loop order. It is shown that the ratio of specific-heat amplitudes at the special and ordinary transitions is given by $\frac{C_{\mathrm{sp}}^0}{C_{\mathrm{ord}}^0}=-1+O\left({\epsilon }^2\right)$. A trajectory integral approach is used to evaluate the crossover for the energy density and specific heat to one-loop order.